Is mathematics 'entangled' with its various formalisations? Or arethe central conceptsof mathematics largely insensitivetoformalisation, or 'formalism free'? What is the semantic point of view and how is it implemented in foundational practice? Does a given semantic framework always have an implicit syntax? Inspired bywhat she calls the 'natural language moves' of Gödeland Tarski, Juliette Kennedy considers what rolesthe concepts of 'entanglement' and 'formalism freeness' play in a range oflogical settings, from computability and set theory to model theory and second order logic, to logicality, developing an entirely original philosophy of mathematics along the way. Thetreatment is historically, logically and set-theoretically rich, andtopics such as naturalism and foundations receive their due, but now with a new twist.